The Magician's Own Book, or, the Whole Art of Conjuring / Being a complete hand-book of parlor magic, and containing over one thousand optical, chemical, mechanical, magnetical, and magical experiments, amusing transmutations, astonishing sleights and subtleties, celebrated card deceptions, ingenious tricks with numbers, curious and entertaining puzzles, together with all the most noted tricks of modern performers.

by George Arnold; Frank Cahill

Ans. 21 ⁵¹⁸³/₅₈₅₈ cents.

Note.—It is usual also, to give smaller prizes to the holders of tickets having the numbers in any order, or having any two or one of the drawn numbers. Lotteries may be arranged on a great diversity of plans, and in each the probability of drawing prizes will vary.

A speaks the truth 3 times in 4; B 4 times in 5, and C 6 times in 7. What is the probability of an event which A and B assert, and C denies? Ans. ¹⁴⁰/₁₄₃

Suppose a coin be thrown up, having two faces; what is the probability that the obverse (heads) side will fall upward, and what the reverse?

Here there are only two possible cases, and one favors each of the contingencies the probability of each will be ¹/_{(1 + 1)} = ¹/₂; there being no reason why one side should fall uppermost rather than the other.

What would be the probability of either side presenting upwards twice in two throws?

Here we have 4 possible cases, viz.:

Obverse and reverse;
Obverse both times;
Reverse and obverse;
Reverse both times.

Of the 4 possibilities there is only one which favors the turning up of the obverse twice in succession, and the same is true of the reverse, hence the probability of either is only ¹/₄.

In like manner we might show that the probability of the obverse presenting upwards three times in succession will be ¹/₈, or ¹/₂ × ¹/₂ × ¹/_2; the general principle being to multiply successively together the independent probabilities of an event for the fraction expressing the chance of all the events happening.